The

*Macaulay duration*is the

**weighted average maturity of a bond**, where the weights are the present values (as a percentage of the bond's price) of the cash flow. Hull's Table 4.6 below illustrates this nicely; the Macaulay duration of his 3-year bond is 2.653 years, which the sum of the right-hand column values, each of which is the product of a PV cash flow and its weight.

Questions (please do not conduct a forum search, as these questions summarize years of forum threads!):

- As Macaulay Duration is the bond's weighted average maturity, we comfortably express Mac duration in years; e.g., Macaulay duration of 2.653 years. So much that, upon reading (for example) "bond duration of 7.0 years" the connotation is Macaulay.

**But what are the UNITS of modified duration and why?** - What is the difference between
*Macaulay*duration,*modified*duration and*effective*duration; especially effective duration? (Best answers are brief but mathematically precise and decisive)